15-59 The device pictured in the following figure entertains infants while keeping them fromwandering. The child bounces in a harness suspended from a door frame by a spring.Figure 15.34 (credit: Lisa Doehnert)What is the angular velocity of the baby?(GRACT[Select]What is the time for one complete bounce of this child?T = [Select]fWhat is the frequency of the baby?[Select] If the spring stretches 0.250 m while supporting an 8.0-kg child, what is its force constant?k = [Select]What is the child's maximum velocity if the amplitude of her bounce is 0.200 m?Vmax[Select]What is the child's maximum acceleration if the amplitude of her bounce is 0.200 m?amaz[Select]

Name: 15-59 The device pictured in the following figure entertains infants
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Description: 15-59 The device pictured in the following figure entertains infants while keeping them fromwandering. The child bounces in a harness suspended from a door frame by a spring.Figure 15.34 (credit: Lisa Doehnert)What is the angular velocity of the bab

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15-59 The device pictured in the following figure entertains infants while keeping them from wandering. The child bounces in a harness suspended from a door frame by a spring. (GRACE) Figure 15.34 (credit: Lisa Doehnert) What is the angular velocity of the baby? w = [Select] What is the time for one complete bounce of this child? T = [Select] What is the frequency of the baby? f [Select]

15-59 The device pictured in the following figure entertains infants while keeping them from wandering. The child bounces in a harness suspended from a door frame by a spring. (GRACE) Figure 15.34 (credit: Lisa Doehnert) What is the angular velocity of the baby? w = [Select] What is the time for one complete bounce of this child? T = [Select] What is the frequency of the baby? f [Select]

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter10: Fixed-axis Rotation

Section: Chapter Questions

Problem 115AP: A pendulum consists of a rod of length 2 m and mass 3 kg with a solid sphere of mass 1 kg and radius...

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A pendulum consists of a rod of mass 2 kg and length 1 m with a solid sphere at one end with mass 0.3 kg and radius 20 cm (see the following figure). If the pendulum is released from rest at an angle of 30 , what is the angular velocity at the lowest point?
When there is a global heating trend on Earth, the atmosphere expands and the length of the day increases very slightly. Explain why the length of a day increases.
Figure P10.18 shows the drive train of a bicycle that has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady cadence of 76.0 rev/min. The chain engages with a from sprocket 15.2 cm in diameter and a rear sprocket 7.00 cm in diameter. Calculate (a) the speed of a link of the chain relative to the bicycle frame, (b) the angular speed of the bicycle wheels, and (c) the speed of the bicycle relative to the road, (d) What pieces of data, if any, are not necessary for the calculations?
Figure P10.16 shows the drive train of a bicycle that has wheels 67.3 cm in diameter and pedal cranks 17.5 cm long. The cyclist pedals at a steady cadence of 76.0 rev/min. The chain engages with a front sprocket 15.2 cm in diameter and a rear sprocket 7.00 cm in diameter. Calculate (a) the speed of a link of the chain relative to the bicycle frame, (b) the angular speed of the bicycle wheels, and (c) the speed of the bicycle relative to the road. (d) What pieces of data, if any, are not necessary for the calculations? Figure P10.16
Check Your Understanding Identify an object that undergoes uniform circular motion. Describe how you could trace the SHM of this object.
A uniform solid sphere of mass m and radius r is releasedfrom rest and rolls without slipping on a semicircular ramp ofradius R r (Fig. P13.76). Ifthe initial position of the sphereis at an angle to the vertical,what is its speed at the bottomof the ramp? FIGURE P13.76
A smaller disk of radius r and mass m is attached rigidly to the face of a second larger disk of radius R and mass M as shown in Figure P15.48. The center of the small disk is located at the edge of the large disk. The large disk is mounted at its center on a frictionless axle. The assembly is rotated through a small angle from its equilibrium position and released. (a) Show that the speed of the center of the small disk as it passes through the equilibrium position is v=2[Rg(1cos)(M/m)+(r/R)2+2]1/2 (b) Show that the period of the motion is v=2[(M/2m)+R2+mr22mgR]1/2 Figure P15.48
Consider two cylinders that start down identical inclines from rest except that one is frictionless. Thus one cylinder rolls without slipping, while the other slides frictionlessly without rolling. They both travel a sh01t distance at the bottom and then start up another incline. (a) Show that they both reach the same height on the other incline, and that this height is equal to their original height. (b) Find the ratio of the time the rolling cylinder takes to reach the height on the second incline to the time the sliding cylinder takes to reach the height on the second incline. (c) Explain why the time for the rolling motion is greater than that for the sliding motion.
A pendulum consists of a rod of length 2 m and mass 3 kg with a solid sphere of mass 1 kg and radius 0.3 m attached at one end. The axis of rotation is as shown below. What is the angular velocity of the pendulum at its lowest point if it is released from rest at an angle of 30 ?
Repeat Example 10.15 in which the stick is free to have translational motion as well as rotational motion.
A nylon siring has mass 5.50 g and length L = 86.0 cm. The lower end is tied to the floor, and the upper end is tied to a small set of wheels through a slot in a track on which the wheels move (Fig. P18.76). The wheels have a mass that is negligible compared with that of the siring, and they roll without friction on the track so that the upper end of the string is essentially free. Figure P18.76 At equilibrium, the string is vertical and motionless. When it is carrying a small-amplilude wave, you may assume the string is always under uniform tension 1.30 N. (a) Find the speed of transverse waves on the siring, (b) The string's vibration possibilities are a set of standing-wave states, each with a node at the fixed bottom end and an antinode at the free top end. Find the node-antinode distances for each of the three simplest states, (c) Find the frequency of each of these states.
Problem: The blade of a fan is 0.20 m long and makes 20 revolutions/seconds. a) What is the period of the motion of the blade? Given: 10 rev f = 4s Solution: Find a) T-2 b) r- 0.3 m, i, - ? c) m= 3g = 0.003 kg , Fe = ? d) ā. -? b) What is its tangential velocity? i, - ? Solutions: 2(3.1416)(0.8m) 0.4 a) What is its period? T-? (5.027m) 0.4s T- T-1 0 re T- 0.4 s 12.57 c) How much force is acting the ball to keep it in uniform circular motion? Fe =? (0.003kg)(12.57: d) What is the centripetal acceleration of the ball? a. -? ā, - (12.57)- 0.8 m m2 0.8 m (0.003kg)(158.0049 158.0049 0.8 m 0.B m (0474 kg 플) - 1975.06 %3D 0.8 m Fe = 0.5925 N